Activist hedge-fund manager Daniel Loeb is ramping up his fight with Sotheby's, even as the art auction house posts stronger sales and profits.

Mr. Loeb nominated himself and two others to Sotheby's board of directors early Thursday, setting up a potentially distracting fight for shareholder votes. The move came hours before the company said its profit jumped 37% in the fourth quarter amid strong sales of Asian and Impressionist...